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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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% In the following statements, replace "Time of talk",
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  4:10 p.m., Tuesday, October 30, 2007\\
  %% Example: 4:15 p.m., Tuesday, February 13, 2007\\
  60 Evans Hall, Berkeley\\
  (There will be refreshments at 3:30 and reception after the talk, both at 1011 Evans Hall)
  %%(Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Andrea Montanari} \\
  Departments of Electrical Engineering and Statistics\\
  Stanford University
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  \subsection*{  Estimating random variables from random sparse observations}
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\noindent

 Let $X_1,\dots, X_n$ be a collection of iid discrete random variables
          and $Y_1,\dots, Y_m$ a set of noisy observations of such variables.
          Assume each observation to be a random function of a random
          subset of the $X_i$'s. We consider the problem of estimating
          the $X_i$'s from such observations.
          This setting encompasses a large array of challenging problems
          arising in communications, computer science and statistics.
          I will describe several examples including sparse graph coding,
          counting in satisfiability problems, and group testing.
          I will then prove a few mathematical properties of such systems that
          arise in the limit of a large number of variables and discuss their
          implications.


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